Jose Pimentel "didn't have the predisposition or the ability to do anything on his own", FBI officials told AP. Photograph: Pool/Getty Images

The FBI did not pursue a case against an alleged al-Qaida sympathiser accused of plotting to blow up police and military personnel because it believed he was mentally unstable and incapable of pulling it off, officials said on Monday.

Investigators from the New York Police Department, which announced the arrest of Dominican-born US citizen Jose Pimentel, 27, at a press conference late on Sunday night, sought to involve the FBI at least twice.

But both times the FBI concluded he wasn't a serious threat, according to officials who spoke to the Associated Press.

Pimentel "didn't have the predisposition or the ability to do anything on his own," said one of the officials, who spoke on condition of anonymity.

The FBI's New York office declined to comment when asked about the case on Monday.

The absence of the FBI from the case was significant because terrorism-related charges are generally prosecuted in federal rather than state court.

Details of the agency's doubts emerged as Pimentel's mother, Carmen Sosa, apologised for her son.

Sosa, 56, broke down in tears and told reporters that he had changed in 2001 after he embraced Islam.

Sosa said she had brought her son to Manhattan from his home in Schenectady in upstate New York because she didn't like the way he was acting.

She said: "I don't know what's going on. I just want peace," she said. "I just want to say I love him, [but] I didn't raise him that way. He changed."

New York state authorities claim Pimentel was planning a plot to build and detonate bombs against police and returning US troops, motivated by terrorist groups and resentment of troops in Iraq and Afghanistan.

The president of the Sergeant's Benevolent Association (SBA), the largest police union in New York, said that the FBI's lack of involvement in the case did not mean Pimentel was not a significant threat.

Sergeant Ed Mullins said: "It does and it doesn't. If we look at the breakdown in capabilities, the FBI are capably of dealing with things of a higher order and on foreign soil. We are better equipped to dealing with things in New York City. On a scale of one to five, with five being the greatest, maybe this is a number two. Maybe the FBI deals with people on a five."

"I think it's reasonable to believe, in terms of how their resources would be best utilised, maybe this is not a threat to national security. But this is a threat to New York. You can't leave unstable individuals purchasing the material to make bombs."

At Sunday's press conference, he was described as a "total lone wolf", by Michael Bloomberg, the mayor of New York.

Police commissioner Raymond Kelly said police, who had Pimentel under surveillance for two years, had to move quickly because he had already bought bomb-making equipment.

"He was, in fact, putting this bomb together," Kelly said. "He was drilling holes, and it would have been not appropriate for us to let him walk out the door with that bomb."

Asked why federal authorities were not involved in the case, Manhattan district attorney Cyrus Vance said there was communication with them, but his office felt that given the timeline "it was appropriate to proceed under state charges."

Pimentel's lawyer, Joseph Zablocki, said his client's behaviour leading up to his arrest on Saturday was not that of a conspirator trying to conceal some violent scheme.

Zablokci said his client was public about his activities and had not tried to hide anything.

"I don't believe that this case is nearly as strong as the people believe," Zablokci told CBS. "He has this very public online profile … This is not the way you go about committing a terrorist attack."

"I don't know whether there's an entrapment issue at this point. It's not outside the realm of possibility that there are other people involved."

On a YouTube channel linked to him, Pimentel – who also goes by the name Muhammad Yusaf – he describes himself as a "Sunni Muslim brother" from the Dominican Republic living in Harlem, whose interests include "watching videos of YouTube, working out, reading and learning all aspects of the only true religion of all the prophets: Islam."